

Article
Secondary flow in spanwiseperiodic inphase sinusoidal channels
Authors: 
Vidal, A., Nagib, H.M., Schlatter, P., Vinuesa, R. 
Document Type: 
Article 
Pubstate: 
Published 
Journal: 
Journal of Fluid Mechancis 
Volume: 
851
288316 
Year: 
2018 
AbstractDirect numerical simulations (DNSs) are performed to analyze the secondary flow of Prandtl's second kind in fully developed spanwiseperiodic channels with inplane sinusoidal walls. The secondary flow is characterized for different combinations of wave parameters defining the wall geometry at Re h = 2500 and 5000, where h is the halfheight of the channel. The total crossflow rate in the channel Q yz is defined along with a theoretical model to predict its behavior. Interaction between the secondary flow from opposite walls is observed if λ h A, where A and λ are the amplitude and wavelength of the sinusoidal function defining the wall geometry. As the outerscaled wavelength (λ/h) is reduced the secondary vortices become smaller and faster, increasing the total crossflow rate per wall. However, if the innerscaled wavelength (λ +) is below 130 viscous units the crossflow decays for smaller wavelengths. By analyzing cases in which the wavelength of the wall is much smaller than the halfheight of the channel λ << h, we show that the crossflow distribution depends almost entirely on the separation between the scales of the instantaneous vortices, where the upper and lower bounds are determined by λ/h and λ + , respectively. Therefore, the distribution of the secondary flow relative to the size of the wave at a given Re h can be replicated at higher Re h by decreasing λ/h and keeping λ + constant. The mechanisms that contribute to the mean crossflow are analyzed in terms of the Reynolds stresses and using quadrant analysis to evaluate the probability density function of the bursting events. These events are further classified with respect to the sign of their instantaneous spanwise velocities. Sweeping events and ejections are preferentially located in the valleys and peaks of the wall, respectively. The sweeps direct the instantaneous crossflow from the core of the channel towards the wall, turning in the walltangent direction towards the peaks. The ejections drive the instantaneous crossflow from the nearwall region towards the core. This preferential behavior is identified as one of the main contributors to the secondary flow.

